Gab and Van can mow the lawn in 40 minutes if they work together. If Gab works twice as fast as Van, how long does it take Gab to mow the lawn alone ?
20 minutes because twice as fast of 20 is 40
20*2=40
time taken by Gab ---- x minutes
time taken by Van ---- 2x minutes
Gab's rate = 1/x
Van's rate = 1/2x
combined rate = 1/x + 1/(2x)
= 3/(2x)
so 1/(3/2x) = 40
2x/3 = 40
2x = 120
x = 60
Gab's time alone is 60 minutes, Van's time alone is 120 minutes
check:
combined time = 1/60 + 1/120
= 3/120 = 1/40
time at combined rate = 1/(1/40) = 40
To find out how long it takes Gab to mow the lawn alone, we can first calculate the rate at which Gab and Van work together. Let's assume that Van's rate of work is V lawns per minute. Since Gab works twice as fast as Van, Gab's rate of work is 2V lawns per minute.
Now, when Gab and Van work together, their rates of work add up. So their combined rate of work is:
V + 2V = 3V lawns per minute
We are given that together they can mow the lawn in 40 minutes. So we now have the equation:
(3V) * 40 = 1 lawn
Simplifying the equation gives us:
120V = 1
To find Van's rate of work, we can divide both sides of the equation by 120:
V = 1/120 lawns per minute
Now that we have Van's rate of work, we can calculate Gab's rate of work. Since Gab works twice as fast as Van, we have:
Gab's rate of work = 2V = 2 * (1/120) = 1/60 lawns per minute
Finally, to find out how long it takes Gab to mow the lawn alone, we can use Gab's rate of work. Since rate is defined as work per unit time, Gab can complete 1 lawn in 1/60 minutes. Therefore, it takes Gab 1/60 minutes to mow the lawn alone.